Journal of Applied Probability

Asymptotic properties of a leader election algorithm

Ravi Kalpathy, Hosam M. Mahmoud, and Mark Daniel Ward

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We consider a serialized coin-tossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically, it turns out to be a geometric distribution. Rice's method (an analytic technique) shows that the moments of the duration contain oscillations, which we give explicitly for the mean and variance. We also use convergence in the Wasserstein metric space to show that the distribution of the total number of coin flips (among all participants), suitably normalized, approaches a normal limiting random variable.

Article information

J. Appl. Probab., Volume 48, Number 2 (2011), 569-575.

First available in Project Euclid: 21 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability
Secondary: 05C05: Trees 60F05: Central limit and other weak theorems 68W40: Analysis of algorithms [See also 68Q25]

Leader election analytic combinatorics Rice's method fixed point contraction method Wasserstein metric space weak convergence


Kalpathy, Ravi; Mahmoud, Hosam M.; Ward, Mark Daniel. Asymptotic properties of a leader election algorithm. J. Appl. Probab. 48 (2011), no. 2, 569--575. doi:10.1239/jap/1308662645.

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